Was Einstein's Method Deductive?

https://www.marxists.org/reference/a...ative/ap03.htm
Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison.. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms."

"Built up logically from a small number of fundamental assumptions" implies that the theory can be presented as a set of arguments, each having one or more premises and a conclusion which is a logical (deductive) consequence of the premises.

Can Einstein's special relativity be presented in this way? His general relativity? The answer to the first question is "yes", to the second is "no". General relativity is not a deductive theory - it is an empirical model. (Einstein and his mathematical friends changed and fudged equations countless times until "a classified catalogue" was compiled where known in advance results and pet assumptions, such as the Mercury's precession, the equivalence principle, gravitational time dilation, coexisted in an apparently consistent manner.)

A truly deductive theory fails if an initial premise (axiom, postulate) is false or if an argument is invalid (the conclusion does not follow from the premises). In the case of special relativity, both failure reasons are actual:

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ECTRODYNAMICS OF MOVING BODIES, A. Einstein, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

Why is the moving clock slow and the stationary one fast? No such asymmetry follows from Einstein's 1905 postulates. What validly follows is that the moving clock is slow as judged from the stationary system, and the stationary clock is slow as judged from the moving system. Einstein's conclusion above (the moving clock "lags behind" the stationary one) should be rejected - it cannot be deduced from the postulates. In other words, the assumption that Einstein's 1905 constant-speed-of-light postulate is true (actually this postulate is false) does not VALIDLY lead to the conclusion that one of the clocks OBJECTIVELY shows less time elapsed than the other.

Pentcho Valev

http://www.forbes.com/sites/startswi...an-we-find-it/
Sabine Hossenfelder: "The Standard Model and General Relativity do a great job, but physicists know this can’t be it. Or at least they think they know: the theories are incomplete, not only disagreeable and staring each other in the face without talking, but inadmissibly wrong, giving rise to paradoxa with no known cure. There has to be more to find, somewhere. But where?"

So Einstein's general relativity is "inadmissibly wrong", and Einsteinians are looking for the source of wrongness. If general relativity were a deductive theory, the advice would be straightforward: Look for a false initial postulate or an invalid argument (there can be no other source of wrongness)! However general relativity is not deductive - it is an empirical model (in this sense it is not even wrong). The making of general relativity was analogous to "curve fitting" ("empirical models") as defined he

http://collum.chem.cornell.edu/docum...ve_Fitting.pdf
"The objective of curve fitting is to theoretically describe experimental data with a model (function or equation) and to find the parameters associated with this model. Models of primary importance to us are mechanistic models. Mechanistic models are specifically formulated to provide insight into a chemical, biological, or physical process that is thought to govern the phenomenon under study. Parameters derived from mechanistic models are quantitative estimates of real system properties (rate constants, dissociation constants, catalytic velocities etc.). It is important to distinguish mechanistic models from empirical models that are mathematical functions formulated to fit a particular curve but whose parameters do not necessarily correspond to a biological, chemical or physical property."

Note that the parameters of the empirical model "do not necessarily correspond to a biological, chemical or physical property". So in Einstein's general relativity one of the parameters - the speed of light falling towards the source of gravity - absurdly DECREASES (in the gravitational field of the Earth the acceleration of falling photons is NEGATIVE, -2g):

http://www.physlink.com/Education/AskExperts/ae13.cfm
"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. (...) ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). (...) You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm
"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential φ would be c(1+φ/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+φ. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. (...) ...we have c_r =1+2φ, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

http://physics.stackexchange.com/que...tational-field
John Rennie: The variation of the velocity of light with distance from the black hole looks like:

http://i.stack.imgur.com/XlKh0.gif

Here Michel Janssen describes endless empirical fudging and fitting until "excellent agreement with observation" was reached:

https://netfiles.umn.edu/users/janss...0page/EBms.pdf
Michel Janssen: "But - as we know from a letter to his friend Conrad Habicht of December 24, 1907 - one of the goals that Einstein set himself early on, was to use his new theory of gravity, whatever it might turn out to be, to explain the discrepancy between the observed motion of the perihelion of the planet Mercury and the motion predicted on the basis of Newtonian gravitational theory. (...) The Einstein-Grossmann theory - also known as the "Entwurf" ("outline") theory after the title of Einstein and Grossmann's paper - is, in fact, already very close to the version of general relativity published in November 1915 and constitutes an enormous advance over Einstein's first attempt at a generalized theory of relativity and theory of gravitation published in 1912. The crucial breakthrough had been that Einstein had recognized that the gravitational field - or, as we would now say, the inertio-gravitational field - should not be described by a variable speed of light as he had attempted in 1912, but by the so-called metric tensor field. The metric tensor is a mathematical object of 16 components, 10 of which independent, that characterizes the geometry of space and time. In this way, gravity is no longer a force in space and time, but part of the fabric of space and time itself: gravity is part of the inertio-gravitational field.. Einstein had turned to Grossmann for help with the difficult and unfamiliar mathematics needed to formulate a theory along these lines. (...) Einstein did not give up the Einstein-Grossmann theory once he had established that it could not fully explain the Mercury anomaly. He continued to work on the theory and never even mentioned the disappointing result of his work with Besso in print. So Einstein did not do what the influential philosopher Sir Karl Popper claimed all good scientists do: once they have found an empirical refutation of their theory, they abandon that theory and go back to the drawing board. (...) On November 4, 1915, he presented a paper to the Berlin Academy officially retracting the Einstein-Grossmann equations and replacing them with new ones. On November 11, a short addendum to this paper followed, once again changing his field equations. A week later, on November 18, Einstein presented the paper containing his celebrated explanation of the perihelion motion of Mercury on the basis of this new theory. Another week later he changed the field equations once more. These are the equations still used today. This last change did not affect the result for the perihelion of Mercury. Besso is not acknowledged in Einstein's paper on the perihelion problem. Apparently, Besso's help with this technical problem had not been as valuable to Einstein as his role as sounding board that had earned Besso the famous acknowledgment in the special relativity paper of 1905. Still, an acknowledgment would have been appropriate. After all, what Einstein had done that week in November, was simply to redo the calculation he had done with Besso in June 1913, using his new field equations instead of the Einstein-Grossmann equations. It is not hard to imagine Einstein's excitement when he inserted the numbers for Mercury into the new expression he found and the result was 43", in excellent agreement with observation."

Pentcho Valev

Einstein's general relativity can predict anything Einsteinians want it to predict, and in this sense it is not even wrong. The reason is that, even though mathematically complex, general relativity is an empirical model:

http://www.nybooks.com/daily/2016/01...ght-and-wrong/
"In 1917 Einstein published a paper on the application of the theory of relativity to the universe at large—cosmology. He had decided that the universe was stationary—neither expanding nor contracting—so he added a term, the cosmological constant, to his original equations with a value of the constant, the Λ in the above equation, chosen to guarantee this. He abandoned this once it was shown in the 1920s by Edwin Hubble that the universe was actually expanding. Now it has been shown that the universe is expanding at an accelerating rate—so the cosmological term is given a new value, the dark energy, now adjusted to produce the acceleration."

Typical empirical approach isn't it? Unlike special relativity, general relativity was not, to use Einstein's words, "built up logically from a small number of fundamental assumptions". Rather, it was "a purely empirical enterprise" - Einstein and his mathematical friends changed and fudged equations countless times until "a classified catalogue" was compiled where known in advance results and pet assumptions (such as the Mercury's precession, the equivalence principle, gravitational time dilation) coexisted in an apparently consistent manner:

https://www.marxists.org/reference/a...ative/ap03.htm
Albert Einstein (1920): "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms."

Pentcho Valev

Einstein informs the gullible world that his approach was deductive:

https://www.marxists.org/reference/a...ative/ap03.htm
"From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction.. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms." x

Einstein is blatantly lying of course - his general relativity was the result of purely empirical gropings (changing and fudging equations until maximum fit with known in advance results and pet assumptions is reached):

https://en.wikipedia.org/wiki/Fudge_factor
"A fudge factor is an ad hoc quantity introduced into a calculation, formula or model in order to make it fit observations or expectations. Examples include Einstein's Cosmological Constant, dark energy, dark matter and inflation. (...) In theoretical physics, when Einstein originally tried to produce a general theory of relativity, he found that the theory seemed to predict the gravitational collapse of the universe: it seemed that the universe should either be expanding or collapsing, and to produce a model in which the universe was static and stable (which seemed to Einstein at the time to be the "proper" result), he introduced an expansionist variable (called the Cosmological Constant), whose sole purpose was to cancel out the cumulative effects of gravitation."

The introduction of a fudge factor is only safe in the case of an empirical model. If the theory is deductive, the need for a fudge factor would mean that some conclusion deduced from the axioms in the absence of the fudge factor is wrong or absurd, and that accordingly at least one of the axioms is false.

Again: The deductive approach is incompatible with activities of this kind:

http://www.scientificamerican.com/ar...science-video/
"Einstein, for instance, assumed the universe must be static, rather than shrinking or expanding, so he added a term called the cosmological constant to his general relativity equations to force it to be so. When it was later revealed the universe was in fact growing larger, he abandoned the term. Yet his initial error led to a second one, because scientists have since revived his constant as a possible explanation for the fact that the universe is not only expanding, but apparently doing so at an accelerating rate."

Pentcho Valev